H2 model matching feedforward control for tape head positioning servo systems

Increasing track densities on tape is a critical step to improve the areal storage capacity and the data transfer rate of tape storage technology. The tape industry envisions increasing track densities from 5,000 tracks per inch (TPI) to more than 50,000 TPI in the next decade. The higher track densities reduce the track pitch significantly and require the tape head servo system to position the read/write head assembly more precisely. While tape transports longitudinally, the tape moves in the lateral direction as well and this motion causes displacements between the head and the desired track. In order to improve the performance of the head positioning servo system to meet the requirements of higher track densities, the disturbance due to the lateral tape motion (LTM) has to be addressed. This paper applies H₂ model matching methods to find an optimal feedforward controller that minimizes the norm of the transfer function from the disturbance to the position error. The existence of a non-trivial solution to the model matching problem is discussed, considering the dynamics of the plant and the disturbance. To constrain the size of the feedforward input to the tape head actuator, the H₂ model matching problem is augmented to minimize the variance of the position error and the size of a weighted norm on the feedforward control simultaneously. Simulation results are presented to demonstrate the effectiveness of the feedforward control, provided a solution exists.